Find the solution of the differential equation y '' = y'e ^ y satisfying the condition y (0) = 0, y '(0) = 1

Find the solution of the differential equation y '' = y'e ^ y satisfying the condition y (0) = 0, y '(0) = 1

Let y '= P, then y' '= DP / DX = DP / dy × dy / DX = P * DP / Dy, and substitute it into the original equation to get p * DP / dy = P * e ^ y. because in the initial condition, y' (0) = 1, that is, P = 1, so p ≠ 0